Question

One bag contains three white marbles and five black marbles, and a second bag contains four white marbles and six black marbles. A person draws one marble from each bag. Find the probability that both marbles are of the same color?

Answer 1

So we have to find two probabilities and add them together, the probability of drawing two whites plus the probability of drawing two blacks...

P(WW)=(3/8)(4/10)=12/80=3/20

P(BB)=(5/8)(6/10)=30/80 so

P(WW or BB)=12/80+30/80=42/80

42/80=21/40 (52.5%)

Answer 2

Probability of both the marbles be of same color is 21/40.

Explanation:

One bag contains 3 white marbles and 5 black marbles.

Second bag contains 4 white and 6 black marbles.

A person draws one marble from each bag and we have to find the probability that both the marbles are of same color.

Probability of getting both balls white = P(ww) = (3/8)×(4/10) = 3/20

Probability of getting both the balls black = P(bb) = (5/8)×(6/10) = 15/40

Probability of getting either both the balls black or white = 3/20 + 15/40 = 21/40

Therefore the probability of getting both the marbles of same color = 21/40